Table 2.

Symbols and notations used throughout the paper

Symbol	Definition
⊙	Element-wise matrix multiplication
D	The number of variables in the time series
$\mathbf{X}\in {\mathbb{ℝ}}^{T\times D}$	The input matrix of the multivariate time series with missing values
$\mathbf{M}\in {\mathbb{ℝ}}^{T\times D}$	The masking matrix indicating missingness in the input matrix
${\mathit{\delta }}_t\in {\mathbb{ℝ}}^D$	The observation gap at time step t
${\mathit{\gamma }}_t\in {\mathbb{ℝ}}^D$	The temporal decay factor at time step t
$\tilde{\mathbf{X}}$	The precompleted input to the model
W, b	Learnable weighing matrix and the bias vector of linear transformations
${\vec{\mathbf{h}}}_t,{\stackrel{⃖}{\mathbf{h}}}_t$	The hidden states of the bidirectional LSTM
${\vec{\mathbf{c}}}_t,{\stackrel{⃖}{\mathbf{c}}}_t$	The cell states of the bidirectional LSTM
r	The context vector
${\mathbf{\beta }}_t\in {\mathbb{ℝ}}^D$	The coefficient for imputation fusion
${\widehat{\mathbf{x}}}_t,{\widehat{\mathbf{z}}}_t,{\mathbf{y}}_t$	The recurrent, cross-feature, and final imputation